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Journal of Logic and Computation 1994 4(5):811-855; doi:10.1093/logcom/4.5.811
© 1994 by Oxford University Press
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Original Articles

Modal Logic, Transition Systems and Processes

JOHAN VAN BENTHEM, JAN VAN EIJCK and VERA STEBLETSOVA

ILLC, Plantage Muidergracht 24 1018 TV Amsterdam, The Netherlands
CWI, Kruislaan 413 1098 SJ Amsterdam, The Netherlands
Department of Philosophy, University of Utrecht Heidelberglaan 8, 3584 CS Utrecht, The Netherlands

Transition systems can be viewed either as process diagrams or as Kripke structures. The first perspective is that of process theory, the second that of modal logic. This paper shows how various formalisms of modal logic can be brought to bear on processes. Notions of bisimulation can not only be motivated by operations on transition systems but can also be suggested by investigations of modal formalisms. To show that the equational view of processes from process algebra is closely related to modal logic, we consider various ways of looking at the relation between the calculus of basic process algebra and propositional dynamic logic. More concretely, the paper contains preservation results for various bisimulation notions, a result on the expressive power of propositional dynamic logic, and a definition of bisimulation which is the proper notion of invariance for concurrent propositional dynamic logic.

Keywords: Modal logic; transition systems; bisimulation; process algebra.


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